Extrapolation of perturbation-theory expansions by self-similar approximants

TL;DR

This paper explores the use of self-similar approximation theory to effectively extrapolate asymptotic perturbation expansions to large variable values, demonstrating its versatility across applied mathematics problems.

Contribution

It introduces and analyzes various self-similar approximants as a novel method for extrapolating perturbation expansions to infinity.

Findings

Self-similar approximants effectively extrapolate asymptotic expansions.

The method applies to diverse problems in applied mathematics.

Self-similar approximants outperform traditional extrapolation techniques.

Abstract

The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures.